First, consider the case in which the neighborhood size is so large that each spin is connected with all other spins in the network. In this case, we recover Granovetter's threshold model for collective behavior [1]}, with dynamics in which the probability of a spin being updated from minus to plus is given by \(\mathbb {P}(\uparrow |y)=(1-y)F(y)\) , where \(y\)  denotes the proportion of plus spins and \(F(\cdot )\)  is the cumulative distribution function of the thresholds' PDF \(f(x)\) :
\(F(x)=\int _{-\infty }^x f(\xi )\mathrm {d}\xi \;.\) 
